PENALTY-FINITE ELEMENT METHODS FOR THE ANALYSIS OF STOKESIAN FLOWS*

A study of a class of finite element methods for the analysis of Stokes’ problem based on the use of exterior penalty formulations is described. The effects of selective reduced integration (i.e., the use of quadrature rules for integrating the penalty terms which are of lower order than that required to integrate polynomial approximations of these terms exactly) are investigated. Error estimates are derived and the numerical stability of these methods, as depicted by a special Babuska-Brezzi condition, is explored in some detail. The results of several numerical experiments with these methods are also given.

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